Best container to move prized records between homes? Thanks!

I used standard small heavy duty moving boxes and moved them in a UHaul. 95% of furnishings professionally moved.  Then again, I drove 1500 miles without stopping to sleep.

U-Haul Boxes either regular or heavy duty.  Each record size box will hold about 100 LPs.  Then then are HEAVY.  I would suggest you use a pallet.  You will be able to fit 12 boxes per pallet.  Wrap with cling wrap and short of the truck crashing and burning, you should be 100% protected.  

The Classic is Orange crates. You can get them free from your local supermarket. 

Last time I shifted a large record collection I had double walled cardboard boxes custom made cost was not much more than regular boxes.

Trick was to keep the boxes smaller in terms of numbers of records so that they are easy to lift and additional rigidity when stacked.

Successfully moved across country on pallet with no issues ( shipped as top stow only - nothing on top ). You can get pallet crates if you cannot trust your shipper to not stack anything on top.

I've used Per Madsen racks for decades. Additional benefit is they can be moved without taking lps out and transferred to another container. Expensive but very satisfying.